Stereo sound separation into three sources

Whenever we listen stereo songs, one part of the audio like voice hear at the center of the head, and other parts are nearby left ear and right ear. If I represent center part by C, and other parts by L' and R', We may model our original left and right channel as,

L' + C = L and,

R' + C = R.

As, common part of L and R channel comes in C vector, L' and R' are uncorrelated. Now we can say, (alpha + beta = pi/2)

Is this modelling correct as per the listening scenario for stereo sound?

Partially correct. Human auditory spatial perception is rather complicated. A good book on the topic would be Spatial Hearing. How and where we localize things depends on a great many factors. For left/right localization the main effects are interaural time difference and interaural level difference. Time differences is the strongest queue. Whatever comes earlier on the left ear will be solidly localized on the left unless even if the sound is louder on the right (within reason). If left & right signals are perfectly time aligned than your model is simplified model.

• I have to work on studio recording audio. I am hoping there L and R channels are at the same distance and they are not adding any delay factor between the channels.
– hari
Sep 25, 2012 at 9:34
• Many recording engineers use inter channel time delay and or temporal effect as artistic means. If you can describe your specific application and what you want to use the mode for, I may be able to assess whether it's applicable or not Sep 25, 2012 at 23:17
• Application is like a 2 to 5 channel upmix. I am looking to design an algorithm where we can separate the L' content and put towards Surround Left channel and simultaneously for right channel. I am trying to separate the common signal content in L and R channel and would like to put in Center channel. If we say that, there is a delay between L and R channel, it means at a particular time instant, there would be very little common in between, the we hear all signals towards either L and R channel. In that case, our L' becomes approximately equal to L, and C is approximately zero.
– hari
Sep 26, 2012 at 5:49
• I am also looking once to apply this strategy to separately encode L', R' and C channel in stereo codec. Presently, we encode (L+R/2) and (L-R)/2. I am not too much aware about the decoder side right now, whether after doing more quantization in (L-R)/2 part, we get exact content towards decoder, or there is a possibility of mixing of content between L and R channel. Also, whether ITD preserve even after mid/diff coding?
– hari
Sep 26, 2012 at 5:57